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Jasper De Bock

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12 papers

2 author rows

I&C Journal 2025 Journal Article

Randomness and imprecision: From supermartingales to randomness tests

Gert de Cooman
Floris Persiau
Jasper De Bock

We generalise the randomness test definitions in the literature for both the Martin-Löf and Schnorr randomness of a series of binary outcomes, in order to allow for interval-valued rather than merely precise forecasts for these outcomes, and prove that under some computability conditions on the forecasts, our definition of Martin-Löf test randomness is related to Levin's uniform randomness. We also show that these new randomness notions are, under some computability and non-degeneracy conditions on the forecasts, equivalent to the martingale-theoretic versions we introduced in earlier papers. In addition, we prove that our generalised notion of Martin-Löf randomness can be characterised by universal supermartingales and universal randomness tests.

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ISIPTA Conference 2025 Conference Paper

Robustness quantification: a new method for assessing the reliability of the predictions of a classifier

Adri\'an Detavernier
Jasper De Bock

Based on existing ideas in the field of imprecise probabilities, we present a new approach for assessing the reliability of the individual predictions of a generative probabilistic classifier. We call this approach robustness quantification, compare it to uncertainty quantification, and demonstrate that it continues to work well even for classifiers that are learned from small training sets that are sampled from a shifted distribution.

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UAI Conference 2021 Conference Paper

Sum-product laws and efficient algorithms for imprecise Markov chains

Jasper De Bock
Alexander Erreygers
Thomas Krak

We propose two sum-product laws for imprecise Markov chains, and use these laws to derive two algorithms to efficiently compute lower and upper expectations for imprecise Markov chains under complete independence and epistemic irrelevance. These algorithms work for inferences that have a corresponding sum-product decomposition, and we argue that many well-known inferences fit their scope. We illustrate our results on a simple epidemiological example.

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IJCAI Conference 2017 Conference Paper

Coherent Predictive Inference under Exchangeability with Imprecise Probabilities (Extended Abstract)

Gert de Cooman
Jasper De Bock
Márcio Alves Diniz

Coherent reasoning under uncertainty can be represented in a very general manner by coherent sets of desirable gambles. This leads to a more general foundation for coherent (imprecise-)probabilistic inference that allows for indecision. In this framework, and for a given finite category set, coherent predictive inference under exchangeability can be represented using Bernstein coherent cones of multivariate polynomials on the simplex generated by this category set. We define an inference system as a map that associates a Bernstein coherent cone of polynomials with every finite category set. Inference principles can then be represented mathematically as restrictions on such maps, which allows us to develop a notion of conservative inference under such inference principles. We discuss, as particular examples, representation insensitivity and specificity, and show that there is an infinity of inference systems that satisfy these two principles.

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ISIPTA Conference 2017 Conference Paper

Computable Randomness is Inherently Imprecise

Gert Cooman
Jasper De Bock

We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define a notion of computable randomness associated with interval, rather than precise, forecasting systems, and study its properties. The richer mathematical structure that thus arises lets us better understand and place existing results for the precise limit. When we focus on constant interval forecasts, we find that every infinite sequence of zeroes and ones has an associated filter of intervals with respect to which it is computably random. It may happen that none of these intervals is precise, which justifies the title of this paper. We illustrate this by showing that computable randomness associated with non-stationary precise forecasting systems can be captured by a stationary interval forecast, which must then be less precise: a gain in model simplicity is thus paid for by a loss in precision.

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ISIPTA Conference 2017 Conference Paper

Efficient Computation of Updated Lower Expectations for Imprecise Continuous-Time Hidden Markov Chains

Thomas Krak
Jasper De Bock
Arno Siebes

We consider the problem of performing inference with imprecise continuous-time hidden Markov chains, that is, imprecise continuous-time Markov chains that are augmented with random output variables whose distribution depends on the hidden state of the chain. The prefix ‘imprecise’ refers to the fact that we do not consider a classical continuous-time Markov chain, but replace it with a robust extension that allows us to represent various types of model uncertainty, using the theory of imprecise probabilities. The inference problem amounts to computing lower expectations of functions on the state-space of the chain, given observations of the output variables. We develop and investigate this problem with very few assumptions on the output variables in particular, they can be chosen to be either discrete or continuous random variables. Our main result is a polynomial runtime algorithm to compute the lower expectation of functions on the state-space at any given time-point, given a collection of observations of the output variables.

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ISIPTA Conference 2017 Conference Paper

Imprecise Continuous-Time Markov Chains: Efficient Computational Methods with Guaranteed Error Bounds

Alexander Erreygers
Jasper De Bock

Imprecise continuous-time Markov chains are a robust type of continuous-time Markov chains that allow for partially specified time-dependent parameters. Computing inferences for them requires the solution of a non-linear differential equation. As there is no general analytical expression for this solution, efficient numerical approximation methods are essential to the applicability of this model. We here improve the uniform approximation method of Krak et al. (2016) in two ways and propose a novel and more efficient adaptive approximation method. For ergodic chains, we also provide a method that allows us to approximate stationary distributions up to any desired maximal error.

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ISIPTA Conference 2017 Conference Paper

Independent Natural Extension for Infinite Spaces: Williams-Coherence to the Rescue

Jasper De Bock

We define the independent natural extension of two local models for the general case of infinite spaces, using both sets of desirable gambles and conditional lower previsions. In contrast to Miranda and Zaffalon (2015), we adopt Williams-coherence instead of Walley-coherence. We show that our notion of independent natural extension always exists—whereas theirs does not—and that it satisfies various convenient properties, including factorisation and external additivity.

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ECAI Conference 2016 Conference Paper

Exploiting Bayesian Network Sensitivity Functions for Inference in Credal Networks

Janneke H. Bolt
Jasper De Bock
Silja Renooij

A Bayesian network is a concise representation of a joint probability distribution, which can be used to compute any probability of interest for the represented distribution. Credal networks were introduced to cope with the inevitable inaccuracies in the parametrisation of such a network. Where a Bayesian network is parametrised by defining unique local distributions, in a credal network sets of local distributions are given. From a credal network, lower and upper probabilities can be inferred. Such inference, however, is often problematic since it may require a number of Bayesian network computations exponential in the number of credal sets. In this paper we propose a preprocessing step that is able to reduce this complexity. We use sensitivity functions to show that for some classes of parameter in Bayesian networks the qualitative effect of a parameter change on an outcome probability of interest is independent of the exact numerical specification. We then argue that credal sets associated with such parameters can be replaced by a single distribution.

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JAIR Journal 2015 Journal Article

Coherent Predictive Inference under Exchangeability with Imprecise Probabilities

Gert de Cooman
Jasper De Bock
Márcio Alves Diniz

Coherent reasoning under uncertainty can be represented in a very general manner by coherent sets of desirable gambles. In a context that does not allow for indecision, this leads to an approach that is mathematically equivalent to working with coherent conditional probabilities. If we do allow for indecision, this leads to a more general foundation for coherent (imprecise-)probabilistic inference. In this framework, and for a given finite category set, coherent predictive inference under exchangeability can be represented using Bernstein coherent cones of multivariate polynomials on the simplex generated by this category set. This is a powerful generalisation of de Finetti's Representation Theorem allowing for both imprecision and indecision. We define an inference system as a map that associates a Bernstein coherent cone of polynomials with every finite category set. Many inference principles encountered in the literature can then be interpreted, and represented mathematically, as restrictions on such maps. We discuss, as particular examples, two important inference principles: representation insensitivitya strengthened version of Walley's representation invarianceand specificity. We show that there is an infinity of inference systems that satisfy these two principles, amongst which we discuss in particular the skeptically cautious inference system, the inference systems corresponding to (a modified version of) Walley and Bernard's Imprecise Dirichlet Multinomial Models (IDMM), the skeptical IDMM inference systems, and the Haldane inference system. We also prove that the latter produces the same posterior inferences as would be obtained using Haldane's improper prior, implying that there is an infinity of proper priors that produce the same coherent posterior inferences as Haldane's improper one. Finally, we impose an additional inference principle that allows us to characterise uniquely the immediate predictions for the IDMM inference systems.

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NeurIPS Conference 2014 Conference Paper

Global Sensitivity Analysis for MAP Inference in Graphical Models

Jasper De Bock
Cassio de Campos
Alessandro Antonucci

We study the sensitivity of a MAP configuration of a discrete probabilistic graphical model with respect to perturbations of its parameters. These perturbations are global, in the sense that simultaneous perturbations of all the parameters (or any chosen subset of them) are allowed. Our main contribution is an exact algorithm that can check whether the MAP configuration is robust with respect to given perturbations. Its complexity is essentially the same as that of obtaining the MAP configuration itself, so it can be promptly used with minimal effort. We use our algorithm to identify the largest global perturbation that does not induce a change in the MAP configuration, and we successfully apply this robustness measure in two practical scenarios: the prediction of facial action units with posed images and the classification of multiple real public data sets. A strong correlation between the proposed robustness measure and accuracy is verified in both scenarios.

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ECAI Conference 2012 Conference Paper

Recent advances in imprecise-probabilistic graphical models

Gert De Cooman
Jasper De Bock
Arthur Van Camp

We summarise and provide pointers to recent advances in inference and identification for specific types of probabilistic graphical models using imprecise probabilities. Robust inferences can be made in so-called credal networks when the local models attached to their nodes are imprecisely specified as conditional lower previsions, by using exact algorithms whose complexity is comparable to that for the precise-probabilistic counterparts.

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